Robert A. Gore

High-Reynolds number Rayleigh–Taylor turbulence

The turbulence generated in the variable density Rayleigh–Taylor mixing layer is studied using the high-Reynolds number fully resolved 30723 numerical simulation of Cabot and Cook (Nature Phys. 2 (2006), pp. 562–568). The simulation achieves bulk Reynolds number, Re = H Ḣ/ν = 32,000, turbulent Reynolds number, Re t = [ktilde] 2/νϵ = 4600, and Taylor Reynolds number, R λ = 170. The Atwood number, A, is 0.5, and the Schmidt number, Sc, is 1. Typical density fluctuations, while modest, being one quarter the mean density, lead to non-Boussinesq effects. A comprehensive study of the variable density energy budgets for the kinetic energy, mass flux and density specific volume covariance equations is undertaken. Various asymmetries in the mixing layer, not seen in the Boussinesq case, are identified and explained. Hypotheses for the variable density turbulent transport necessary to close the second moment equations are studied. It is found that, even though the layer width becomes temporally self-similar relatively fast, the transient effects in the energy spectrum remain important for the duration of the simulation. Thus, the dissipation does not track the spectral energy cascade rate and the integral lengthscale does not follow the expected Kolmogorov scaling, [ktilde] 3/2/ϵ. As a result, the popular eddy diffusivity expression, ν t ∼[ktilde] 2/ϵ, does not model the temporal variation of the turbulent transport in any of the moment equations. An eddy diffusivity based on a lengthscale related to the layer width is found to work well in a gradient transport hypothesis for the turbulent transport; however, that lengthscale is a global quantity and does not lead to pointwise, local closure. Therefore, although the transient effects may vanish asymptotically, it is suggested that, even long after the onset of the self-similar growth, two separate lengthscale equations (or equivalent) are needed in a moment closure strategy for Rayleigh–Taylor turbulence: one for the turbulent transport and the other for the dissipation. Despite the fact that the intermediate scales are nearly isotropic, the small scales have a persistent anisotropy; this is due to a cancellation between the viscous and nonlinear effects, so that the anisotropic buoyancy production remains important at the smallest scales.

Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids

A second-moment closure model is proposed for describing turbulence quantities in flows where large density fluctuations can arise due to mixing between different density fluids, in addition to compressibility or temperature effects. The turbulence closures used in this study are an extension of those proposed by Besnard et al., which include closures for the turbulence mass flux and density-specific-volume covariance. Current engineering models developed to capture these extended effects due to density variations are scarce and/or greatly simplified. In the present model, the density effects are included and the results are compared to direct numerical simulations (DNS) and experimental data for flow instabilities with low to moderate density differences. The quantities compared include Reynolds stresses, turbulent mass flux, mixture density, density-specific-volume covariance, turbulent length scale, turbulence and material mix time scales, turbulence dissipation, and mix widths and/or growth rates. These comparisons are made within the framework of three very different classes of flows: shear-driven, Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Overall, reasonable agreement is seen between experiments, DNS, and averaging models.

New phenomena in variable-density Rayleigh?Taylor turbulence

This paper presents several issues related to mixing and turbulence structure in buoyancy-driven turbulence at low to moderate Atwood numbers, A, found from direct numerical simulations in two configurations: classical Rayleigh–Taylor instability and an idealized triply periodic Rayleigh–Taylor flow. Simulations at A up to 0.5 are used to examine the turbulence characteristics and contrast them with those obtained close to the Boussinesq approximation. The data sets used represent the largest simulations to date in each configuration. One of the more remarkable issues explored, first reported in (Livescu and Ristorcelli 2008 J. Fluid Mech. 605 145–80), is the marked difference in mixing between different density fluids as opposed to the mixing that occurs between fluids of commensurate densities, corresponding to the Boussinesq approximation. Thus, in the triply periodic configuration and the non-Boussinesq case, an initially symmetric density probability density function becomes skewed, showing that the mixing is asymmetric, with pure heavy fluid mixing more slowly than pure light fluid. A mechanism producing the mixing asymmetry is proposed and the consequences for the classical Rayleigh–Taylor configuration are discussed. In addition, it is shown that anomalous small-scale anisotropy found in the homogeneous configuration (Livescu and Ristorcelli 2008 J. Fluid Mech. 605 145–80) and Rayleigh–Taylor turbulence at A=0.5 (Livescu et al 2008 J. Turbul. 10 1–32) also occurs near the Boussinesq limit. Results pertaining to the moment closure modelling of Rayleigh–Taylor turbulence are also presented. Although the Rayleigh–Taylor mixing layer width reaches self-similar growth relatively fast, the lower-order terms in the self-similar expressions for turbulence moments have long-lasting effects and derived quantities, such as the turbulent Reynolds number, are slow to follow the self-similar predictions. Since eddy diffusivity in the popular gradient transport hypothesis is proportional to the turbulent Reynolds number, the dissipation rate and turbulent transport have different length scales long after the onset of the self-similar growth for the layer growth. To highlight the importance of turbulent transport, variable density energy budgets for the kinetic energy, mass flux and density-specific volume covariance equations, necessary for a moment closure of the flow, are provided.

Detailed high-resolution three-dimensional simulations of OMEGA separated reactants inertial confinement fusion experiments

We present results from the comparison of high-resolution three-dimensional (3D) simulations with data from the implosions of inertial confinement fusion capsules with separated reactants performed on the OMEGA laser facility. Each capsule, referred to as a “CD Mixcap,” is filled with tritium and has a polystyrene (CH) shell with a deuterated polystyrene (CD) layer whose burial depth is varied. In these implosions, fusion reactions between deuterium and tritium ions can occur only in the presence of atomic mix between the gas fill and shell material. The simulations feature accurate models for all known experimental asymmetries and do not employ any adjustable parameters to improve agreement with experimental data. Simulations are performed with the RAGE radiation-hydrodynamics code using an Implicit Large Eddy Simulation (ILES) strategy for the hydrodynamics. We obtain good agreement with the experimental data, including the DT/TT neutron yield ratios used to diagnose mix, for all burial depths of the deuterated shell layer. Additionally, simulations demonstrate good agreement with converged simulations employing explicit models for plasma diffusion and viscosity, suggesting that the implicit sub-grid model used in ILES is sufficient to model these processes in these experiments. In our simulations, mixing is driven by short-wavelength asymmetries and longer-wavelength features are responsible for developing flows that transport mixed material towards the center of the hot spot. Mix material transported by this process is responsible for most of the mix (DT) yield even for the capsule with a CD layer adjacent to the tritium fuel. Consistent with our previous results, mix does not play a significant role in TT neutron yield degradation; instead, this is dominated by the displacement of fuel from the center of the implosion due to the development of turbulent instabilities seeded by long-wavelength asymmetries. Through these processes, the long-wavelength asymmetries degrade TT yield more than the DT yield and thus bring DT/TT neutron yield ratios into agreement with experiment. Finally, we present a detailed comparison of the flows in 2D and 3D simulations.

On primitive variable behaviour near shocks in ensemble-averaged methods

ABSTRACTModels for averaged shock corrugation effects and the impact of turbulent entropy or acoustic modes on the energy equation are presented, for application in Reynolds-Averaged Navier Stokes(RANS) simulations of shock-turbulence interactions. Unlike previous work that has focused the modification of turbulent statistics by the shock, the proposed models are introduced to capture the effects of the turbulence on the profiles of primitive variables - mean density, velocity, and pressure. By producing accurate profiles for the primitive variables, it is shown that the proposed models improve numerical convergence behaviour with mesh refinement about a shock, and introduce the physical effects of shock asphericity in a converging shock geometry. These effects are achieved by local closures to turbulent statistics in the averaged Navier-Stokes equations, and can be applied in conjunction with existing Reynolds stress closures that have been constructed for broader applications beyond shock-turbulence int...

Validating the BHR RANS model for variable density turbulence

The BHR RANS model is a turbulence model for multi-fluid flows in which density variation plays a strong role in the turbulence processes. In this paper they demonstrate the usefulness of BHR over a wide range of flows which include the effects of shear, buoyancy, and shocks. The results are in good agreement with experimental and DNS data across the entire set of validation cases, with no need to retune model coefficients between cases. The model has potential application to a number of aerospace related flow problems.

Effects on Initial Development of Rayleigh-Taylor Instabilities Due to a Change in Initial Conditions

The effect on the initial development of Rayleigh-Taylor mixing due to a change in initial conditions has been experimentally studied. A water channel facility at Texas A&M University has been used to provide a statistically steady experiment for the investigation of buoyancy-driven turbulent mixing. Parallel streams of hot and cold water are separated initially by a splitter plate. The streams are oriented in such a way to place cold water above the hot water. Upon the termination of the splitter plate, the two streams are allowed to mix and a buoyancy-driven mixing layer develops. The growth rate of the mixing layer has been experimentally measured using image analysis techniques. Our studies have shown that introducing broadband initial disturbances can have a significant effect on the growth rate of Raleigh-Taylor instabilities, however, the mechanism that controls energy transfer at early time is not clear and requires further investigation.Copyright